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3 years ago

Given an arithmetic sequence with a3=5 and a5=19, find the 24th term.

Mathematics

1 answer:

krok68 [10]3 years ago

5 0

The 24th term is 152

Step-by-step explanation:

The formula of the nth term of an arithmetic sequence is:

$a_n=a+(n-1)d$ , where

a is the first term
d is the common difference between consecutive terms

The third term means n = 3

∵ $a_3=a+(3-1)d$

∴ $a_3=a+2d$

∵ $a_3$ = 5

- Equate the right hand sides of the third term

∴ a + 2d = 5 ⇒ (1)

The fifth term means n = 5

∵ $a_5=a+(5-1)d$

∴ $a_5=a+4d$

∵ $a_5$ = 19

- Equate the right hand sides of the fifth term

∴ a + 4d = 19 ⇒ (2)

Now we have a system of equations to solve it

Subtract equation (1) from equation (2) to eliminate a

∴ 2d = 14

- Divide both sides by 2

∴ d = 7

- Substitute the value of d in equation (1) to find a

∵ a + 2(7) = 5

∴ a + 14 = 5

- Subtract 14 from both sides

∴ a = -9

The twenty fourth term means n = 24

∵ a = -9 and d = 7

- Substitute the values of a and d in the formula of the nth term

∴ $a_24=-9+(24-1)(7)$

∴ $a_24=-9+(23)(7)$

∴ $a_24=-9+161$

∴ $a_24=152$

The 24th term is 152

Learn more:

You can learn more about the arithmetic sequence in brainly.com/question/7221312

#LearnwithBrainly

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